AP Calculus AB Flashcards: Approximating Areas with Riemann Sums
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
For a strictly increasing function, will a left Riemann sum be an underestimate or an overestimate?
For a strictly increasing function, a left Riemann sum will be an underestimate for the value of the definite integral.
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For a strictly increasing function, will a left Riemann sum be an underestimate or an overestimate?
For a strictly increasing function, a left Riemann sum will be an underestimate for the value of the definite integral.
For a strictly increasing function, will a right Riemann sum be an underestimate or an overestimate?
For a strictly increasing function, a right Riemann sum will be an overestimate for the value of the definite integral.
What is the difference between uniform and nonuniform partitions when computing an approximation?
Approximations can be computed using uniform partitions, where all subintervals have the same width, or nonuniform partitions, where the subintervals can have different widths.
How is a right Riemann sum calculated?
A right Riemann sum approximates the definite integral by using rectangles whose heights are determined by the function's value at the right endpoint of each subinterval.
What are the four common numerical sum methods used to approximate definite integrals?
The four common methods are the left Riemann sum, right Riemann sum, midpoint Riemann sum, and the trapezoidal sum.
How is a left Riemann sum calculated?
A left Riemann sum approximates the definite integral by using rectangles whose heights are determined by the function's value at the left endpoint of each subinterval.
How is a midpoint Riemann sum calculated?
A midpoint Riemann sum approximates the definite integral by using rectangles whose heights are determined by the function's value at the midpoint of each subinterval.
How is a trapezoidal sum calculated?
A trapezoidal sum approximates the definite integral by summing the areas of trapezoids whose parallel sides are determined by the function's values at the endpoints of each subinterval.
What is a Riemann sum?
A Riemann sum is a numerical method used to approximate the value of a definite integral by summing the areas of geometric shapes, typically rectangles or trapezoids, over partitions of an interval.
What determines if a Riemann sum or trapezoidal sum is an underestimate or overestimate?
The behavior of the function, such as whether it is increasing, decreasing, concave up, or concave down, determines if an approximation is an underestimate or overestimate.
From what four types of function representations can definite integrals be approximated?
Definite integrals can be approximated for functions that are represented graphically, numerically (in a table), analytically (with an equation), and verbally.